Scale-up of liquid mixing systems

The principle of similarity [Holland (1964), Johnstone and Thring (1957)] together with the use of dimensionless groups is the essential basis of scale-up. The types of similarity relevant to liquid mixing systems together with their definitions are listed as follows. 

Geometrical similarity exists between two systems of different sizes when the ratios of corresponding dimensions in one system are equal to those in 

Dimensionless groups provide a convenient way of correlating scientific and engineering data. 

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Holland, F.A. Scale-Up of Liquid Mixing Systems, Chemical Engineering, Sept. 17, 1962, p. 179. Chen, S.J., MacDonald, A.R. Motionless Mixers for Viscous Polymers, Chemical Engineering, Mar. 19, 1973, p. 105. 

The scale-up of liquid mixing systems can be divided into two categories the scale-up of process result and the scale-up of power data. 

Lab-scale systems used for experiments are usually completely mixed, especially with respect to the liquid phase. This has been assumed for the following discussion, It simplifies the description of the system hydrodynamics in the models immensely, but often leads to neglect of the system hydrodynamics in the scale-up of lab-scale results for pilot or full-... 

Gas-liquid bubble columns and gas-liquid-solid slurry bubble columns are widely used in the chemical and petrochemical industries for processes such as methanol synthesis, coal liquefaction, Fischer-Tropsch synthesis and separation methods such as solvent extraction and particle/gas flotation. The hydrodynamic behavior of gas-liquid bubble columns and gas-liquid-solid slurry bubble columns are of great importance for the design and scale-up of reactors. Although the hydrodynamics of the bubble and slurry bubble columns has been a subject of intensive research through experiments and computations, the flow structure quantification of complex multi-phase flows are still not well understood, especially in the three-dimensional region. In bubble and slurry bubble columns, the presence of gas bubbles plays an important role to induce appreciable liquid/solids mixing as well as mass transfer. The flows within these systems are divided into two... 

Much of the literature on scale-up of reaction systems has focused on continuous systems. However, scale-up methods for batch and semibatch operations have been included in several books, including Oldshue (1983), Whitaker and Cas-sano (1986) Carberry and Varma (1987) Froment and Bischoff (1990), Tatterson (1991), Hamby et al. (1992), and Baldyga and Bourne (1999). Correlations for heat transfer, mass transfer, Uquid-liquid dispersions, solids suspensions, and dissolntion are available and are discussed iu these references and in several chapters of this book. Mixing requirements for scale-up of homogeneous reactions are discussed in Chapter 13, including explanation of the limitations of the nsnal mixing scale-up parameter of equal power per unit volume. The reader is referred to the texts listed in the references, in which these correlations are well developed. These correlations are not reproduced in this chapter. 

These incubations are often carried out at 37 °C for 1-2 h. At different time points, 20-200 /aL of incubation mixture is withdrawn from each incubation and mixed with equal volume of ice-cold acetonitrile by vortexing. For preparation of acyl glucuronide, ice-cold acetonitrile containing 1% of formic acid is used to minimize acyl-migration [3,14]. After centrifugation at 13 000 rpm for 5-15 min, the supernatant (10-30 /aU) is analyzed by high-performance liquid chromatography (HPUC)-UV-MS. The metabolite of interest is identified based on HPLC retention time, UV spectrum and MS/MS data. Conversion yield is estimated based on UV absorption peak areas. A suitable in vitro enzyme system for scale-up is then... 

Similarly, the superficial velocity v or vq of the gas throughput as an intensity quantity is a reliable scale-up criterion only in mass transfer in gas/liquid systems in bubble columns. In mixing operations in bubble columns, requiring the whole liquid content be back mixed (e.g., in homogenization), this criterion completely loses its validity (10). 

Mixing processes involved in the manufacture of disperse systems, whether suspensions or emulsions, are far more problematic than those employed in the blending of low-viscosity miscible liquids due to the multi-phasic character of the systems and deviations from Newtonian flow behavior. It is not uncommon for both laminar and turbulent flow to occur simultaneously in different regions of the system. In some regions, the flow regime may be in transition, i.e., neither laminar nor turbulent but somewhere in between. The implications of these flow regime variations for scale-up are considerable. Nonetheless, it should be noted that the mixing process is only completed when Brownian motion occurs sufficiently to achieve uniformity on a molecular scale. 

In this chapter, we study various correlations for gas-liquid mass transfer, interfacial area, bubble size, gas hold-up, agitation power consumption, and volumetric mass-transfer coefficient, which are vital tools for the design and operation of fermenter systems. Criteria for the scale-up and shear sensitive mixing are also presented. First of all, let s review basic mass-transfer concepts important in understanding gas-liquid mass transfer in a fermentation system. 

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